Details

Time bar (total: 1.2m)

sample83.0ms

Algorithm
intervals
Results
21.0ms40×body2560valid
14.0ms165×body80valid
13.0ms31×body1280valid
9.0ms108×body80nan
5.0ms16×body640valid
3.0ms5×body5120valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify176.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize38.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* b b) (* (* 3 a) c)))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.0b
(- (* b b) (* (* 3 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
55.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
19.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
15.0ms
(- (* b b) (* (* 3 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
125.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
97.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
66.0ms
(- (* b b) (* (* 3 a) c))

simplify5.1s

Counts
52 → 106
Calls
52 calls:
Slowest
581.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
354.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
338.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
298.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
260.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

localize46.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* b b) (* (* 3 a) c)))
16.1b
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
1.0b
(- (* b b) (* (* 3 a) c))
0.3b
(* 3 (* c a))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
45×add-cbrt-cube add-exp-log
21×prod-exp cbrt-unprod
10×pow1
9×cbrt-undiv div-exp
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down sqrt-prod flip--
2×sqrt-div associate-*r/ associate-/r/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 times-frac pow1/2 fma-neg diff-log associate-*r* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 92
Calls
4 calls:
Slowest
46.0ms
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
14.0ms
(* 3 (* c a))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms
(- (* b b) (* (* 3 a) c))

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
106.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
58.0ms
(- (* b b) (* (* 3 a) c))
24.0ms
(* 3 (* c a))

simplify12.5s

Counts
53 → 104
Calls
53 calls:
Slowest
4.2s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
505.0ms
(- (+ (log 3) (+ (log c) (log a))) (+ (+ (log 3) (log a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
480.0ms
(- (+ (log 3) (log (* c a))) (+ (+ (log 3) (log a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
473.0ms
(* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a)))
448.0ms
(- (+ (log 3) (+ (log c) (log a))) (+ (log (* 3 a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize43.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* b b) (* (* 3 a) c)))
13.7b
(/ (* 3 (* c a)) (* 3 a))
1.0b
(- (* b b) (* (* 3 a) c))
0.3b
(* 3 (* c a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
12×prod-exp cbrt-unprod
10×pow1
7×add-sqr-sqrt
6×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*l* pow-prod-down sqrt-prod
2×flip3-- sqrt-div flip--
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 times-frac pow1/2 fma-neg diff-log associate-*r* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
Slowest
24.0ms
(/ (* 3 (* c a)) (* 3 a))
18.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
12.0ms
(* 3 (* c a))
7.0ms
(- (* b b) (* (* 3 a) c))

series195.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
62.0ms
(- (* b b) (* (* 3 a) c))
37.0ms
(* 3 (* c a))
7.0ms
(/ (* 3 (* c a)) (* 3 a))

simplify23.5s

Counts
44 → 96
Calls
44 calls:
Slowest
4.8s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
4.2s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
2.9s
(- (+ (log 3) (log (* c a))) (+ (log 3) (log a)))
1.8s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 3) 3) (* (* a a) a)))
1.7s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize41.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* b b) (* (* 3 a) c)))
1.0b
(- (* b b) (* (* 3 a) c))
0.3b
(- (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(* (* 3 a) c)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×pow1 add-log-exp
9×add-cbrt-cube add-exp-log
7×neg-mul-1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- diff-log associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 147
Calls
4 calls:
Slowest
25.0ms
(* (* 3 a) c)
22.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms
(- (* b b) (* (* 3 a) c))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 3 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
78.0ms
(- (* b b) (* (* 3 a) c))
20.0ms
(* (* 3 a) c)

simplify21.0s

Counts
165 → 159
Calls
165 calls:
Slowest
485.0ms
(* -3/2 (/ (* a c) b))
429.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
400.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
382.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
357.0ms
(fma (- 1) b (- (* (cbrt (sqrt (- (* b b) (* (* 3 a) c)))) (* (cbrt (sqrt (- (* b b) (* (* 3 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3 a) c))))))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

regimes459.0ms

Accuracy

94.3% (1.3b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.2b

bsearch373.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
950.0ms2921×body80nan
905.0ms1034×body2560valid
874.0ms5891×body80valid
635.0ms855×body1280valid
301.0ms468×body640valid
132.0ms108×body5120valid
78.0ms221×body320valid
31.0ms127×body160valid